Albert B. Fletcher Jr., the U.S. Court of Military Appeals judge who was convicted on a morals charge and fined $500 earlier this year in Fairfax County Circuit Court, has asked President Reagan to grant him early retirement for medical reasons.

The military court's chief judge, Robinson O. Everett, and Fletcher's lawyer, Stephen R. Pickard of Alexandria, both said Fletcher, who turned 60 yesterday, requested that he be excused from the bench after his conviction.

Fletcher, who underwent open heart surgery in February of last year, was "really, really sick at the time" of his arrest by Fairfax County police last fall, Pickard said in an interview. His retirement request is based on physical ailments, according to a knowledgeable source.

Fletcher would receive about one-third of his $82,500 annual salary if he is permitted to retire for medical reasons, Everett said. The chief judge said Fletcher's term on the court is scheduled to end next May 1 and that his retirement might take effect then.

Fletcher has appealed his Feb. 27 felony conviction on a charge that he solicited an undercover Fairfax County police officer last October to perform a homosexual act in a park along the George Washington Parkway. No date has been set for arguments in the case, which will be heard by the Virginia Court of Appeals, according to Pickard.

Pickard said he will attempt to challenge the constitutionality of the Virginia law governing sexual solicitation and the sufficiency of the evidence used to convict his client.

Fletcher, a former state judge in Kansas, was appointed to the Court of Military Appeals in 1975 by President Ford and served as chief judge from then until 1980. He has not returned to work since his arrest although, Everett said, "his vote has been recorded on some matters heard before the incident."

Fletcher's absence has left his two colleagues on the three-judge court short-handed, Everett added. The court receives about 3,000 new cases a year, from the armed forces' military courts.